Minimizing decision table sizes in influence diagrams: dimension shrinking

One goal in evaluating an influence diagram is to compute an optimal decision table for each decision node. More often than not, one is able to shrink the sizes of some of the optimal decision tables without any loss of information. This paper investigates when the opportunities for such shrinkings arise and how can we detect them as early as possible so as to to avoid unnecessary computations. One type of shrinking, namely dimension shrinking, is studied. A relationship between dimension shrinking and what we call lonely arcs is established, which enables us to make use of the opportunities for dimension shrinking by means of pruning lonely arcs at a preprocessing stage.